Indirect field-oriented control (IFOC) is commonly used control method for a three-phase induction machine (IM). If motor parameters of the IM are known, the IFOC reduces the complex IM dynamics to the dynamics of a separately excited dc machine. Using this approach allows the flux and torque of the induction machine to be controlled independently.
The induction machine model used in IFOC controller is given by the following equations:                               ω          s                =                                            ω              e                        -                          ω              r                                =                                                    R                r                                            L                r                                      ⁢                                                   ⁢                          M                              Ψ                dr                                      ⁢                                                   ⁢                          i              qs                                                          (        1        )                                                                    R              r                        ⁢                                                   ⁢                          Ψ              dr                                +                                    L              r                        ⁢                                                   ⁢                                          ⅆ                                                                   ⁢                                  Ψ                  dr                                                            ⅆ                t                                                    =                              R            r                    ⁢                                           ⁢          M          ⁢                                           ⁢                      i            ds                                              (        2        )                                          T          e                =                              3            /            2                    ⁢                                           ⁢          P          ⁢                                           ⁢                      M                          L              r                                ⁢                                           ⁢                      (                                          Ψ                dr                            ⁢                                                           ⁢                              i                qs                                      )                                              (        3        )            In equations (1)-(3), ids and iqs are flux and torque producing stator current components, respectively. Ψdr is a rotor flux magnitude.
The assumption of the IFOC is that Ψdr=0 and that the stator current components are controlled by the current control loop. Rr is a rotor resistance, M is a mutual inductance, and Lr=M+Llr is a rotor inductance. Llr is a rotor leakage inductance and Llr<<M. Also, ωe is a stator electrical frequency, ωe is a rotor electrical frequency, ωs is a slip frequency, and Te is a produced torque.
The performance of the IFOC is sensitive to discrepancies between estimated machine parameters used by the IFOC and actual machine parameters. During operation, the actual machine parameters drift from nominal or estimated values due to changes in operating conditions. If the estimated parameters stored in the IFOC controller do not reflect the actual machine parameters, a parameter mismatch occurs. As a result, the machine flux level is not properly maintained. Torque response linearity is also lost. In other words, produced torque is different from the commanded value. The discrepancy also typically exists in steady-state conditions. Finally, the torque response to step torque command is not instantaneous.
The mutual inductance M and the rotor resistance Rr have a significant impact on the performance of the IFOC. The mutual inductance M varies significantly with the machine saturation level. The variation of the mutual inductance with the flux level can be compensated using look-up tables that may be obtained during off-line characterization. The rotor resistance Rr is predominantly influenced by rotor temperature. Since the rotor temperature varies with machine operating conditions, the rotor resistance must be estimated using on-line approaches for tracking the rotor resistance variations during machine operation.
Referring now to FIG. 1, the commanded values for flux and torque producing stator current components ids* and iqs* respectively, are inputs to an IFOC 20. The IFOC 20 outputs reference voltages, va, vb and vc, which are fed to a power inverter 24 of an induction motor 26. A calculating circuit 34 calculates a function y from measured quantities, including voltages va, vb and vc and phase currents ia, ib, and ic. The same function is calculated in IFOC by using the internal variables and is denoted as {tilde over (y)}.
A difference, e={tilde over (y)}−y, that is generated by a difference circuit 48 is input to an adaptation controller 50. The output of the adaptation controller 50 determines the rotor resistance value Rr that is used in IFOC 20. If the function y is sensitive to the rotor resistance, any difference between the motor Rr value and the IFOC Rr value produces a non-zero error (e={tilde over (y)}≠−0). The non-zero error will force the Rr value used in IFOC to change.
Conventional IFOC use several different functions including: reactive power (Q); electromagnetic torque (Te); active power (P); a ratio of reactive power and electromagnetic torque (Q/Te); and, a scalar product of transposed rotor flux vector and stator current vector (ΨrTis). These functions, however, are not sufficiently sensitive to changes in the rotor resistance Rr or are impractical for real-time implementation. As a result, parameter drift and reduced performance occurs.